I recall back in the day there was at least one game for the 8-bit NES that required more than one cartridge to play. Likely it asked for the second one at some point along the way, you swapped, and continued on. I don't recall the name or objective of this game. Does anyone else? I tried searching google for it and instead the results kept directing me to various cartridges that had multiple games on them.

Perhaps one of the Nobunaga's Ambition titles? It seems like it would lend itself better to a game with highly linear play.